How to use it
An auditory illusion is a sound that you hear differently from what a measuring instrument would record, because the brain interprets what reaches the ears. Pick one of six classic examples with the tabs, press Play and compare what you hear with the picture of what is physically in the sound. Start with the volume low.
Controls
- Choosing an illusion: click or tap a tab, or use the left and right arrow keys or the number keys 1 to 6. Switching stops the sound.
- Play and Stop: the button under the picture or the Space bar. One volume slider serves everything.
- Settings: the sliders and switches below the picture act while the sound plays and are saved in this browser.
- Tritone paradox: press Play pair, then answer “Went up” or “Went down” (keys U and D).
- Headphones check: two buttons play a short tone in one ear only.
How it works
Shepard tone. Each note is a stack of eight sine waves spaced exactly one octave apart. A fixed bell-shaped curve over a logarithmic frequency scale sets their loudness: loud in the middle, fading to nothing at both ends.
ai = ½ − ½ cos(2πx), x = log2(fi / 32.7 Hz) / 8
When the scale rises, every component moves up. The highest fades out while a new one fades in at the bottom, so after twelve semitones the sound is exactly the first note again. Roger Shepard described these tones in 1964; Jean-Claude Risset made the continuous, gliding version. The ear follows each step but cannot tell which octave it is in.
Tritone paradox. Two Shepard tones exactly half an octave (six semitones) apart are played in turn. Each has a clear note name but no definite octave, so the second is equally far above and below the first. Diana Deutsch reported in 1986 that listeners still hear a definite direction, that it depends on the starting note, and that people disagree. Her later studies linked the pattern to the language or dialect a listener grew up with.
Missing fundamental. The sound contains the harmonics 2f0, 3f0, 4f0 and so on, with no energy at f0. The waveform still repeats f0 times per second, and hearing takes pitch from that repetition and from the even spacing of the harmonics, so the pitch stays at f0. This is why a deep voice keeps its pitch on a traditional telephone line, which carries almost nothing below about 300 Hz.
Binaural beats. The left ear gets a steady tone of frequency f, the right ear a steady tone of f + d. Neither changes in loudness, yet a slow wobble is heard d times per second. It is thought to arise in the brainstem, where the signals from the two ears are first compared. Mixed into the same ear, the two tones add up physically and the loudness really rises and falls d times per second. Heinrich Wilhelm Dove described binaural beats in 1839.
Octave illusion. Tones of 400 Hz and 800 Hz alternate four times a second, always in opposite ears, so each ear receives high, low, high, low. Diana Deutsch discovered in 1973 that most people instead hear a single tone that jumps: high in one ear, then low in the other. Her explanation: the brain decides “what” and “where” separately, taking the pitch from one dominant ear and the position from the ear that gets the higher tone.
Continuity illusion. A tone with silent gaps sounds chopped. Fill the gaps with noise loud enough to have drowned out the tone, and the tone seems to carry on through the noise, although it is still absent. The ear gets no evidence that the tone stopped, so the brain settles on the simplest story: a steady tone behind the noise.
Things to try
- Shepard tone: switch to the continuous glide and watch one bar leave at one edge while another enters at the other.
- Missing fundamental: set f0 to 100 Hz on a phone speaker and compare with the pure tone, which a small speaker can barely reproduce.
- Binaural beats: take one earphone out and the beat is gone. With both tones in both ears it survives.
- Octave illusion: listen to each ear alone, then both. Swap left and right and check whether the high tone changes sides.
- Continuity illusion: fill the gaps with noise, then lower the noise level until the tone breaks up again.
Frequently asked questions
Do I need headphones?
For binaural beats and the octave illusion, yes: each ear must get its own signal. The other four also work on loudspeakers. The page cannot detect what you are listening on.
Which tritone answer is correct?
Neither. A tritone is exactly half an octave, so “up” and “down” describe the same pair equally well. Compare your chart with a friend’s.
Do binaural beats improve focus, sleep or mood?
Such claims are not supported by solid evidence, and this page makes none. The effect is shown here only as a demonstration of how the two ears work together.
Why does an illusion not work for me?
People differ. Some listeners hear the octave illusion in another pattern, and the continuity illusion needs noise clearly louder than the tone.